Journal of South China University of Technology(Natural Science) >
Investigation into Critical Depth in Silo-Grains-Lifting Rod Systems Based on Janssen's Continuum Model
Received date: 2023-12-04
Online published: 2024-04-28
Supported by
the Guizhou Provincial Basic Research Program (Natural Science)(ZK2022148)
Granular matter is widely present in nature and human production and life. It exhibits many mechanical properties that differ from those of conventional solids and liquids. Janssen effect is one of the important and well-known phenomena that demonstrates the unique static mechanical properties of granular matter. Researchers have conducted in-depth studies on this effect from various perspectives, including theoretical models and computer simulations. “Chopstick rice-lifting” is an interesting physical phenomenon closely related to the Janssen effect. However, existing research lacks a quantitative analysis of this phenomenon, particularly regarding the discussion of the critical depth. In this paper, the actual system involved in “chopstick rice-lifting” is simplified into a system composed of a silo, grains, and a lifting rod, and the Janssen continuum model is employed to conduct a static mechanical analysis of this system, leading to the theoretical derivation of a transcendental equation concerning the critical depth. Subsequently, by combining experimental data with the numerical solution of this transcendental equation, the authors explore how the Janssen coefficient and critical depth of the granular system in the experiment vary with relevant physical quantities. The results indicate that the Janssen coefficient under different experimental conditions fluctuates slightly around an average value 1.16; and that, when the diameter of the lifting rod is held constant, an increase in the diameter and mass of the silo results in a higher total mass of both the grains and the silo, thereby increasing the critical depth. Conversely, when the diameter of the silo is constant, an increase in the diameter of the lifting rod leads to a decrease in the total mass and an increase in the contact area between the lifting rod and the grains, resulting in a decrease in the critical depth. The theoretical calculation results are generally consistent with the experimental measurement results.
ZHANG Xinggang , CUI Jinqin , HE Ninghuai , TANG Yan , CUI Jinhe , WANG Feng . Investigation into Critical Depth in Silo-Grains-Lifting Rod Systems Based on Janssen's Continuum Model[J]. Journal of South China University of Technology(Natural Science), 2024 , 52(12) : 87 -92 . DOI: 10.12141/j.issn.1000-565X.230752
| 1 | 陆坤权,刘寄星 .颗粒物质(上)[J].物理,2004,33(9):629-635. |
| LU Kun-quan, LIU Ji-xing .Static and dynamic properties of granular matter (Ⅰ)[J].Physics,2004,33(9):629-635. | |
| 2 | 丁小彬,施钰,陈俊生 .基于三维离散元的大直径钢圆筒下沉侧摩阻力[J].华南理工大学学报(自然科学版),2020,48(4):15-27. |
| DING Xiaobin, SHI Yu, CHEN Junsheng .Side friction of large-diameter steel cylinder simulated using 3D discrete element method[J].Journal of South China University of Technology (Natural Science Edition),2020,48(4):15-27. | |
| 3 | 张兴刚,戴丹,汤燕 .单分散圆盘堆积的Voronoi统计模型[J].华南理工大学学报(自然科学版),2023,51(2):122-130. |
| ZHANG Xinggang, DAI Dan, TANG Yan .Statistical Voronoi model for monodisperse disk packings[J].Journal of South China University of Technology (Natural Science Edition),2023,51(2):122-130. | |
| 4 | 李湘群,蒋亦民,彭政,等 .Rankine被动应力状态粮仓的Janssen行为[J].山东大学学报(理学版),2010,45(9):101-105. |
| LI Xiang-qun, JIANG Yi-min, PENG Zheng,et al .Janssen behavior of a grain silo in a Rankine passive stress state[J].Journal of Shandong University (Science Edition),2010,45(9):101-105. | |
| 5 | 王璐珠,蒋亦民,彭政,等 .非Jaky粮仓的弹性应力分析和侧壁边界条件[J].科学通报,2011,56(14):1091-1096. |
| WANG Luzhu, JIANG Yimin, PENG Zheng,et al .Boundary condition and elastic analysis of stress for silos without Jaky property[J].Scientific Bulletin,2011,56(14):1091-1096. | |
| 6 | 胡林,杨平,徐亭,等 .颗粒物质中圆棒受到的静摩擦力[J].物理学报,2003,52(4):879-882. |
| HU Lin, YANG Ping, XU Ting,et al .The static friction force on a rod immersed in granular matter[J].Acta Physica Sinica,2003,52(4):879-882. | |
| 7 | 孔维姝,胡林,杜学能,等 .用探测棒研究颗粒堆中的最大静摩擦力[J].物理学报,2007,56(4):2318-2322. |
| KONG Wei-shu, HU Lin, DU Xue-neng,et al .Studies of maximum static friction force in granular pile with probing rod[J].Acta Physica Sinica,2007,56(4):2318-2322. | |
| 8 | 白光富,胡林,张忠政,等 .小筒仓内颗粒中探测棒受到的最大静摩擦力[J].力学与实践,2009,31(4):64-68. |
| BAI Guangfu, HU Lin, ZHANG Zhongzheng,et al .Static friction force on probing rod in granular pile in small container[J].Mechanics and Practice,2009,31(4):64-68. | |
| 9 | 李智峰,彭政,蒋亦民 .粮仓内颗粒压力的测量:Janssen行为及其偏差[J].物理学报,2014,63(10):296-303. |
| LI Zhi-feng, PENG Zheng, JIANG Yi-min .Measurements of granular pressure in silo:Janssen behaviour and deviation[J].Acta Physica Sinica,2014,63(10):296-303. | |
| 10 | 冯云田,华云龙 .适用于柔性圆筒仓的修正的Janssen公式[J].中国农业大学学报,1996,1(4):107-111. |
| FENG Yuntian, HUA Yunlong .Modified Janssen formula for flexible circular bins[J].Journal of China Agricultural University,1996,1(4):107-111. | |
| 11 | THORENS L, M?L?Y K J, BOURGOIN M,et al .Magnetic Janssen effect[J].Nature Communications,2021,12(1):2486/1-6. |
| 12 | MAHAJAN S, TENNENBAUM M, PATHAK S N,et al .Reverse Janssen effect in narrow granular columns[J].Physical Review Letters,2020,124(12):128002/1-5. |
| 13 | 陈喜山,朱卫东 .Janssen公式的拓广与应用[J].土木工程学报,1996,29(5):11-17. |
| CHEN Xishan, ZHU Weidong .Extension and application of Janssen equation[J].Journal of Civil Engineering,1996,29(5):11-17. | |
| 14 | 郑甲红,明磊,马浩然 .基于Janssen模型的扦样管受力分析与试验[J].粮食储藏,2022,51(5):9-12. |
| ZHENG Jiahong, MING Lei, MA Haoran .Stress analysis and experiment of sampling tube based on Janssen model[J].Grain Storage,2022,51(5):9-12. | |
| 15 | 周新雅,周行,蔡孝文 .基于教材“筷子提米”实验的科学探究与教学实践[J].中学物理教学参考,2018,47(19):66-67. |
| ZHOU Xin-ya, ZHOU Hang, CAI Xiao-wen .Scientific inquiry and teaching practice based on the textbook“Chopsticks-picking-rice”experiment[J].Physics Teaching Reference for Secondary Schools,2018,47(19):66-67. | |
| 16 | 徐秋实,周新雅 .利用颗粒物体之间静摩擦力规律改进筷子提米实验[J].物理教师,2018,39(9):51-53. |
| XU Qiu-shi, ZHOU Xin-ya .Improvement of chopsticks-picking-rice experiment using the laws of static friction between granular particles[J].Physics Teacher,2018,39(9):51-53. | |
| 17 | ZHANG X, DAI D .Exact solutions for Janssen effect of lattice disk packings[J].Powder Technology,2023,420:118380/1-10. |
| 18 | BLANCO-RODRíGUEZ R, PéREZ-áNGEL G .Stress distribution in two-dimensional silos[J].Physical Review E,2018,97(1-1):012903/1-10. |
| 19 | VIVANCO F, MERCADO J, SANTIBá?EZ F,et al .Stress profile in a two-dimensional silo:effects induced by friction mobilization[J].Physical Review E,2016,94(2):022906/1-9. |
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